In 2007, Tachiya gave necessary and sufficient conditions for the transcendence of certain infinite products involving Fibonacci numbers Fk and Lucas numbers Lk. In the present note, we explicitly evaluate two classes of his algebraic examples. Special cases are
n = 1(1+1F2n+1) = 3φ,  n = 1(1+1L2n+1) = 3−φ,
where φ = (1+5)/2 is the golden ratio.
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